Abstract
In this evolutionary model, random shocks create differences in the rate of return on capital, while individual saving and investment behavior can reduce these differences over time. Firms with either low total factor productivity (TFP) or a low average return on capital are selected for exit, and new firms enter to take their place. As would be expected, a higher turnover rate improves TFP and reduces its variation. While we show that a higher turnover rate would result in a more positively skewed TFP distribution if exit selection is based directly upon TFP, we find that when we select firms for exit based on their average product of capital, the marginal impact of a higher turnover rate is to more negatively skew the TFP distribution. Overall, our simulations highlight the importance of considering the role selection may play in shaping the distribution of productivity when econometricians seek estimates of firm inefficiency.
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Notes
In doing so, we are following Jovanovic (1982), who cites evidence that small firms grow faster than large firms but are also more likely to fail, and creates a model of “‘noisy’ selection” to explain why.
As of June, 2001, when this research began, Econlit listed 217 citations for the stochastic frontier approach since 1977, and 365 citations for the data envelopment approach since 1985. In the past few years, citations for the former approach are around half those for the latter approach, suggesting that the former method is gradually being replaced by the latter.
See, for example, Ericson and Pakes (1995) for a description and model of this process.
Cargill and Parker (2002) used a simulation of a Walrasian tattonment process, but it is computationally demanding.
Parker (1995) and Cargill and Parker (2002) assumed that this shock was exponentially normal, of the form \(a_{{it}} = a_{{i,t - 1}} \;e^{{\varepsilon _{{it}} }}\). While this has the benefit of ensuring that TFP is always positive, it biases the results towards a positive skew. However, we tested the simulation in Section 4 by re-running it with the exponential shock; in re-estimating the response function, we found the marginal effects not significantly affected.
Of course, bankruptcy as a legal process is rarely so optimal. Managers may be willing to continue operating a loss-making firm if they can hide information on the firm’s poor long-run potential from the owners. Creditors with first priority of repayment may force a potentially productive firm to liquidate to ensure that they do not have to accept a loss on their investment.
We chose 20 iterations because it was long enough to observe changes in the distribution of productivity. We also tested whether our results were sensitive to this duration by rerunning our results for 50 iterations. While coefficient values obviously changed, the sign and statistical significance of these coefficients, as reported in Tables 3, 4, and 5, did not change in either the end or trend regressions.
We thank the editor for raising the issue of changing the number of firms. An interesting extension of this work would be to change the assumptions of the model so that the number of firms is endogenously determined, say by replacing constant returns to scale with decreasing returns. Then, one could systematically examine how changing the economic environment not only changes the number of firms in an economy with selection, but also changes the mean, variance and skew of total factor productivity.
The changes in these preference parameters did not significantly influence the results.
We simulated the estimation of current consumption with different parameter sets for many values of Z. We found that consumption estimates were wildly unstable for values of Z below 5, so the stable arm of the growth path is clearly not linear. However, for Z≥10, we found that the consumption estimates started to converge asymptotically. The estimates obtained for Z=25 were very close to the estimates for T=10,000.
Each case is a separate simulation, and small differences are to be expected due to differences in the random shocks.
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Parker, E., Pingle, M. The distributional effects of selection and capital accumulation on firm productivity under imperfect capital markets. Empirical Economics 31, 677–697 (2006). https://doi.org/10.1007/s00181-005-0046-1
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DOI: https://doi.org/10.1007/s00181-005-0046-1